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 J. Sib. Fed. Univ. Math. Phys., 2011, Volume 4, Issue 2, Pages 265–272 (Mi jsfu184)

Conditions for convexity of the isotropic function of the second-rank tensor

Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia

Abstract: For a scalar function, depending on the invariants of the second-rank tensor, condition of convexity and strong convexity are obtained with respect to the components of this tensor in an arbitrary Cartesian coordinate system. It is shown that if a function depends only on the four invariants: three principal values of the symmetric part of a tensor and modulus of pseudovector of the antisymmetric part, these conditions are necessary and sufficient. A special system of convex invariants is suggested to construct potentials for the stresses and strains in the mechanics of structurally inhomogeneous elastic media, exhibiting moment properties.

Keywords: isotropic tensor function, convexity, invariants, nonlinear elasticity, plasticity.

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UDC: 517.17+539.37
Accepted: 10.12.2010

Citation: Vladimir M. Sadovskii, “Conditions for convexity of the isotropic function of the second-rank tensor”, J. Sib. Fed. Univ. Math. Phys., 4:2 (2011), 265–272

Citation in format AMSBIB
\Bibitem{Sad11} \by Vladimir~M.~Sadovskii \paper Conditions for convexity of the isotropic function of the second-rank tensor \jour J. Sib. Fed. Univ. Math. Phys. \yr 2011 \vol 4 \issue 2 \pages 265--272 \mathnet{http://mi.mathnet.ru/jsfu184}